CEGUI::Quaternion Class Reference

Class to represent rotation, avoids Gimbal lock. More...

Inheritance diagram for CEGUI::Quaternion:

Collaboration diagram for CEGUI::Quaternion:

Public Member Functions
	Quaternion (float w=1.0f, float x=0.0f, float y=0.0f, float z=0.0f)
	verbatim constructor
	Quaternion (const Quaternion &v)
	copy constructor
Quaternion &	operator= (const Quaternion &v)
	assignment operator
bool	operator== (const Quaternion &v) const
	equality operator
bool	operator!= (const Quaternion &v) const
	inequality operator
Quaternion	operator- () const
	negation operator
Quaternion	operator* (float v) const
	scalar multiplication operator
float	dot (const Quaternion &v) const
	quaternion dot product
Quaternion	operator+ (const Quaternion &v) const
	addition operator
Quaternion	operator* (const Quaternion &v) const
	quaternion multiplication (not commutative!) More...
float	length () const
	computers and returns the length of this quaternion
float	normalise ()
	normalises this quaternion and returns it's length (since it has to be computed anyways)

Static Public Member Functions
static Quaternion	eulerAnglesRadians (float x, float y, float z)
	constructs a quaternion from euler angles in radians More...
static Quaternion	eulerAnglesDegrees (float x, float y, float z)
	constructs a quaternion from euler angles in degrees More...
static Quaternion	axisAngleRadians (const Vector3f &axis, float rotation)
	constructs a quaternion from axis and angle around it in radians More...
static Quaternion	axisAngleDegrees (const Vector3f &axis, float rotation)
	constructs a quaternion from axis and angle around it in degrees More...
static Quaternion	slerp (const Quaternion &left, const Quaternion &right, float position, bool shortestPath=false)
	spherical linear interpolation More...

Public Attributes
float	d_w
	imaginary part
float	d_x
	x component of the vector part
float	d_y
	y component of the vector part
float	d_z
	z component of the vector part

Static Public Attributes
static const Quaternion	ZERO
	Quaternion(0, 0, 0, 0)
static const Quaternion	IDENTITY
	Quaternion(1, 0, 0, 0)

Friends
Quaternion	operator* (float v, const Quaternion &q)
	scalar multiplication operator
std::ostream &	operator<< (std::ostream &s, const Quaternion &v)
	allows writing the quaternion to std ostream

Detailed Description

Class to represent rotation, avoids Gimbal lock.

Most people are afraid of Quaternions, you don't have to fully understand them. In CEGUI, you can just think of quaternions as magic opaque boxes that hold rotation data. No need to understand how they work and why. You obviously have to understand what degrees and radians are, I won't go into that here.

How to convert "human readable" rotation data to Quaternions: 1) Euler angles, 3 floating point values x - rotation around X axis (anticlockwise) y - rotation around Y axis (anticlockwise) z - rotation around Z axis (anticlockwise)

The actual rotation is performed in z, y, x order. Keep that in mind!

For these, just use eulerAnglesDegrees or eulerAnglesRadians static methods.

2) Rotation around axis, 1 Vector3 and one degree/radian angle the vector represents the axis (it's length doesn't matter at all), rotation is then performed by rotating given angle anticlockwise around that axis.

For these, use axisAngleDegrees or axisAngleRadians static methods.

Member Function Documentation

static Quaternion CEGUI::Quaternion::axisAngleDegrees ( const Vector3f &  axis, float  rotation  )

static

constructs a quaternion from axis and angle around it in degrees

Parameters

axis	vector describing the axis of rotation
rotation	Anticlockwise rotation around given axis

static Quaternion CEGUI::Quaternion::axisAngleRadians ( const Vector3f &  axis, float  rotation  )

static

constructs a quaternion from axis and angle around it in radians

Parameters

axis	vector describing the axis of rotation
rotation	Anticlockwise rotation around given axis

static Quaternion CEGUI::Quaternion::eulerAnglesDegrees ( float  x, float  y, float  z  )

static

constructs a quaternion from euler angles in degrees

Parameters

x	Anticlockwise rotation around X axis
y	Anticlockwise rotation around Y axis
z	Anticlockwise rotation around Z axis

The rotation is performed around Z first, then Y and then X!

static Quaternion CEGUI::Quaternion::eulerAnglesRadians ( float  x, float  y, float  z  )

static

constructs a quaternion from euler angles in radians

Parameters

x	Anticlockwise rotation around X axis
y	Anticlockwise rotation around Y axis
z	Anticlockwise rotation around Z axis

The rotation is performed around Z first, then Y and then X!

Quaternion CEGUI::Quaternion::operator* ( const Quaternion &  v ) const

inline

quaternion multiplication (not commutative!)

Lets say we have quaternion A describing a rotation and another quaternion B. If we write C = A * B, C is actually describing a rotation we would get if we rotated Identity by A and then rotated the result by B

References d_w, d_x, d_y, and d_z.

static Quaternion CEGUI::Quaternion::slerp ( const Quaternion &  left, const Quaternion &  right, float  position, bool  shortestPath = false  )

static

spherical linear interpolation

Parameters

left	Left keyframe Quaternion
right	Right keyframe Quaternion
position	Number from range <0.0, 1.0), the closer this is to 1.0, the closer the interpolation is to the "right" quaternion
shortestPath	If true, the interpolation is guaranteed to go through the shortest path